For n ∈ ℕ, we consider the problem of partitioning
the interval [0, n) into k subintervals of positive integer
lengths ℓ1, …, ℓk such that
the lengths satisfy a set of simple constraints of the form
ℓi ◇ij ℓj
where ◇ij is one of <, >,
or =. In the full information case,
◇ij is given for all
1 ≤ i, j ≤ k. In the
sequential information case, ◇ij is
given for all 1 < i < k and
j = i ± 1. That is, only the
relations between the lengths of consecutive intervals are specified. The
cyclic information case is an extension of the sequential information
case in which the relationship ◇1k between
ℓ1 and ℓk is also given. We show
that all three versions of the problem can be solved in time polynomial in
k and log n.